Abstract
We determine the normalisation of scalar and pseudo scalar current operators made from NonRelativistic QCD (NRQCD) b quarks and Highly Improved Staggered (HISQ) light quarks through O(αs∧QCD/mb). We use matrix elements of these operators to extract B meson decay constants and form factors and compare to those obtained using the standard vector and axial vector operators. We work on MILC second-generation 2+1+1 gluon field configurations, including those with physical light quarks in the sea. This provides a test of systematic uncertainties in these calculations and we find agreement between the results to the 2% level of uncertainty previously quoted.
Highlights
The accuracy of the determination of weak decay matrix elements from lattice QCD is critical to the flavour physics programme of over-determination of the Cabibbo-Kobayashi-Maskawa (CKM) matrix in the search for new physics
We study matrix elements for B mesons obtained using the NonRelativistic QCD (NRQCD) formalism for b quarks and the Highly Improved Staggered Quark (HISQ) formalism for light quarks
To determine the B and Bs meson decay constants the authors of [1] calculated the appropriate matrix elements for NRQCD-HISQ current operators on eight different ensembles of gluon fields generated by the MILC collaboration [4]
Summary
The accuracy of the determination of weak decay matrix elements from lattice QCD is critical to the flavour physics programme of over-determination of the Cabibbo-Kobayashi-Maskawa (CKM) matrix in the search for new physics. As well as improving the accuracy where possible, it is important to test the systematic uncertainties by doing the calculations in multiple different ways This includes using different formalisms for the quarks and using different methods for the same formalisms. State-of-the-art calculations were carried out in [1] for the B decay constant using an NRQCD Hamiltonian [2] and a temporal axial current operator both improved through αsΛQCD/mb to obtain a 2% overall uncertainty. This uncertainty was dominated by the perturbative matching of the nonrelativistic current to that in the continuum, which was done using perturbation theory through O(αs). The systematic uncertainties in the semileptonic form factor for B → π ν from the traditional method of using a vector current can be tested by employing a scalar current
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